Theorem 5.1 (Theorem 1 in [1]}) 
Under Condition (A1), it holds with \(\mathbb {P}_0^{(n)}\) -probability at least \(1 - n^{-10}\)  that
\(\Vert \hat{f}_n-f_\lambda \Vert _{\tilde{\mathbb {H}}}\le \frac{\tilde{\kappa }^{-1}C(n,\tilde{\kappa })}{1-C(n,\tilde{\kappa })}\Vert f_\lambda -f_0\Vert _\infty +\frac{1}{1-C(n,\tilde{\kappa })}\frac{4\tilde{\kappa }\sigma \sqrt{20\log n}}{\sqrt{n}},\) 
